House Republicans on Tuesday unveiled an ambitious and politically perilous plan to resize the federal government and stem the $14 trillion national debt by slashing spending on domestic programs and fundamentally overhauling government health programs for the elderly and the poor.

The 2012 budget blueprint would not touch Social Security, the single largest federal program, which provides income support to nearly 60 million seniors, disabled people and others. But with the cost of benefits expected to exceed revenues this year, Republicans say they would enact legislation to force President Obama to propose changes to “restore balance to the fund.” Suggested reforms include adjusting the retirement age to reflect longer life spans and slowing the growth in benefits for higher-income workers.

All told, the document, titled the “Path to Prosperity,” proposes to spend about $40 trillion over the next decade — $6.2 trillion less than the budget that Obama put out in February.

Despite its vast ambitions, however, the blueprint drafted by House Budget Committee Chairman Paul Ryan (R-Wis.) underscores the tremendous difficulty of mopping up the nation’s enormous tide of red ink.

For fiscal 2012, for example, Ryan’s plan would authorize $3.5 trillion in total spending, leaving a budget deficit next year of just under $1 trillion. That’s slightly lower than the deficit projected under current law, but it’s still a significant budget gap.

Annual deficits would dwindle to under $400 billion by the end of the decade, a dramatic improvement over Obama’s budget proposal. But even Ryan’s plan would take nearly 30 years to wipe out deficits completely. More deficits mean more borrowing, and the national debt would keep rising under Ryan’s plan — requiring lawmakers to raise the $14.3 trillion legal limit on borrowing this year. Even Ryan’s austere proposal would allow the debt to rise, to more than $16 trillion next year and more than $23 trillion by 2021.

A significant number of Republicans, however, oppose raising the debt limit. On Monday, Treasury Secretary Timothy Geithner pushed congressional leaders to raise the cap, which he says the country will hit in mid May, forcing it to default.

Because the economy would keep growing, the debt would diminish as a percentage of gross domestic product, an important measure of financial stability that could help the nation avert a debt crisis. But that considerable achievement might be too nuanced for the most conservative members of the House Republican caucus, several of whom berated Obama’s budget director in February for failing to offer a plan that would end additional borrowing.

“The American people understand we can’t continue spending money we don’t have, especially when doing so is making it harder to create jobs and get our economy back on track,” House Speaker John Boehner (R-Ohio) said. “Our budget will help spur job creation today, stop spending money we don’t have and lift the crushing burden of debt that threatens our children’s future.”

Senate Minority Leader Mitch McConnell (R-Ky.) said Ryan’s plan “would put us on a path to reducing the national debt. It would strengthen the social safety net so we can keep the promises we’ve made to America’s seniors. ... And it will repeal last year’s health-care law, which will raise health-care costs, lead to fewer jobs, and which Americans have rejected.”

Democrats saw a ripe opening for attack. “Behind the sunny rhetoric of reform,” Rep. Chris Van Hollen (D-Md.), the senior Democrat on the House Budget Committee, said in a statement, “the Republican budget represents the rigid ideological agenda that extends tax cuts to the rich and powerful at the expense of the rest of America.”

House Minority Leader Nancy Pelosi (D-Calif.) blasted Ryan’s proposal in her Twitter feed, accusing Republicans of seeking to eliminate “guaranteed benefits for seniors under Medicare and calling it “a path to poverty for America’s seniors & children and a road to riches for big oil.”

Some Republicans have already dismissed the Ryan plan as too timid, saying they can’t go back to constituents without a balanced budget. Ryan and House leaders will start selling their proposal to their caucus Tuesday in a closed-door meeting that will also address the impasse over the fiscal 2011 budget. Earlier Tuesday, House leaders announced another short-term spending bill to keep the government open past a deadline this Friday.

However, Republicans emerging from a morning meeting with House leaders Tuesday said they were united behind the Ryan plan. They argued that voters sent Republicans to Washington to rein in spending, even if that means cutting cherished programs for the poor and the elderly.

“This is about making America strong again financially. Political risk must be taken,” said Rep. Morgan Griffith (R-Va.), a tea party-backed freshman.

Freshman Rep. Tim Huelskamp (R-Kan.) added: “We recognize the fear out there and the threat to the future of the American dream, and this is exactly what we were elected to do... This is what we came for: not to talk about small things, but big issues and the future of our country.”

The larger budget battle will begin even before the 2011 fight is resolved. Ryan plans to open a voting session Wednesday on his 2012 blueprint in the House Budget Committee. If approved, the measure would then go to the House floor, where GOP aides declined to speculate on its fate.

If approved by the House, the blueprint would go the Senate, where the Democratic majority is unlikely to accept much of Ryan’s vision for the nation’s fiscal future. Senate Budget Committee Chairman Kent Conrad (D-N.D.) is instead at work with five senators of both parties on a strategy to reduce the debt by triming funds for entitlement programs less dramatically than Ryan’s plan while raising additional revenue through an overhaul of the tax code.

Whatever its fate in Congress, the Ryan plan will serve as a statement of the grandest ambitions of the Republican Party and set the terms of the debate for the 2012 presidential campaign.

The proposal urges a sweeping transformation of federal health programs that would wipe out funding for Obama’s health-care initiative and end Medicare as an open-ended entitlement. Medicare, the federal health program for the elderly, would be replaced for those under age 55 with a system of premium supports to buy insurance policies in the private market. The plan would not restore cuts to Medicare made under Obama’s health- care legislation, though it would eliminate a special board established to restrain the program’s future growth.

Medicaid, the health program for the poor, would come in for sharper cuts, totaling $771 billion over the next decade. The GOP plan would roll back the Medicaid expansion called for under Obama’s health initiative by ending the financing partnership between the federal government and the states. Instead it would create block grants giving states less federal money but freeing them to manage the program as they wish.

“People are living longer. The baby boomers are beginning to retire. Health-care costs are skyrocketing,” the blueprint says. “These are facts, and they require a better approach to renew the social contract.”

On discretionary spending, Ryan’s plan would match Obama’s call for Pentagon and war funding, but it proposes major cuts to domestic programs totaling $1.6 trillion over the next decade — holding growth in education, transportation, justice, food safety and other programs well below the rate of inflation. The move would make good on a Republican campaign pledge to restore domestic spending to levels in effect in 2008, before George W. Bush and Obama began pumping federal dollars into the economy to blunt the effects of recession.

Programs for the poor would get particular attention, the blueprint says, “to ensure that America’s safety net does not become a hammock that lulls able-bodied citizens into lives of complacency and dependency.”

Ryan also proposes to overhaul the tax code, lowering the top rate for individuals and corporations from 35 percent to 25 percent, while eliminating an array of loopholes and deductions that his budget does not identify. GOP aides said they would leave the details to the tax-writing House Ways and Means Committee, which is crafting a tax reform plan that would maintain revenues at historic levels and would not contribute to deficit reduction.

Ryan also rejects calls to raise taxes on high earners to finance Social Security benefits at their current levels, one of the most popular methods of repairing the program’s finances.

“Those who wish to solve this problem by raising taxes are ignoring the profound economic damage that such large tax increases would entail,” his blueprint says. “Just lifting the cap on income subject to Social Security taxes, as some have proposed, would, when combined with the Obama administration’s other preferred tax policies, lift the top marginal tax rate to over 60 percent.”

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